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Some specification for thesis require 10pt quote on a separate line. Assuming that the thesis is written with 12pt is this correct approach to obtain 10pt for quote?

Is any other simple solution?

\documentclass[12pt,a4paper]{report}
\usepackage[utf8]{inputenc}
\usepackage[romanian]{babel}
\usepackage[margin=2.5cm]{geometry}
\usepackage{kantlipsum}

\begin{document}
\kant[1]
\begin{quote}
\footnotesize{\kant[1]}
\end{quote}
\end{document}
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You asked,

Assuming that the thesis is written with 12pt is [\footnotesize the] correct approach to obtain 10pt for quote?

Short answer: Yes. More precisely, it's one among several possible correct approaches to obtaining the desired formatting outcome.

Now on to a longer answer. The report document class defines the option 12pt as follows:

\DeclareOption{12pt}{\renewcommand\@ptsize{2}}

whereby \@ptsize is set to 2. Later on in report.cls, one finds these instructions:

\ProcessOptions
\input{size1\@ptsize.clo}

This (a) executes \renewcommand\@ptsize{2} and (b) inputs the file size12.clo as \@ptsize is expanded to 2.

Next, in the file size12.clo, one finds the following instructions:

\renewcommand\normalsize{%
   \@setfontsize\normalsize\@xiipt{14.5}%
   % (other stuff)
   }

and

\DeclareRobustCommand\footnotesize{%
   \@setfontsize\footnotesize\@xpt\@xiipt
   % (other stuff)
   }

Aside: \@xpt and \@xiipt expand to 10 and 12, respectively.

Long story short: If the report class is loaded with the option 12pt, the main font size -- \normalsize -- is 12pt on 2.5 points of leading, while \footnotesize works out to 10pt on 2 points of leading. ("Leading" is an old-fashioned (archaic??) expression, which refers to the thickness of the strips of lead that were inserted between lines of metal type.)

What to do with all this information?

  • If your document has just one quote environment, it's perfectly alright to insert the instruction \footnotesize right after \begin{quote}.

    Aside: Note that \footnotesize is a switch and doesn't take an argument. Thus, \footnotesize{\kant[1]} is no different from \footnotesize \kant[1]; the latter is preferable since it doesn't create any false impressions.

  • If your document features several quote environments and if they must all be typeset at 10pt, I suggest you load the etoolbox package in the preamble and insert the instruction

    \AtBeginEnvironment{quote}{\footnotesize}
    

    to automate the process of switching to the required font size.

  • If, for some reason, you take pride in making LaTeX execute only the absolutely minimal number of instructions needed to get a given job done, you might observe that \footnotesize actually performs additional instructions -- such as changing the default amount of vertical whitespace that's inserted above and below displayed equations -- besides changing the font size to 10pt on 2pt of leading; it turns out that these additional instructions aren't needed here. Indeed, instead of running \footnotesize, you could also run

    \fontsize{10}{12}\selectfont
    

    to get the desired font size.

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    Excellent explanation for my problem. I will bookmark this answer for future references. For the moment I'll use your solution with etoolbok which is preferable of \newcommand which crossed my mind.
    – Mafsi
    Jan 23 '21 at 9:02

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